Measure out all ingredients and bring the butter and egg to room temperature—this ensures smooth mixing and better texture in your cookies. In a medium bowl, whisk together the flour, cocoa powder, baking soda, and salt. Set this dry mixture aside. Having everything measured and ready will make the next steps flow seamlessly.

In a large bowl, beat the softened butter with the brown sugar and 1/3 cup of granulated sugar for about 2 minutes until light and fluffy. This creaming process incorporates air into the dough, which helps the cookies rise slightly and create a tender texture. Scrape down the bowl halfway through to ensure even mixing.

Add the room temperature egg, vanilla extract, and 1/2 tsp peppermint extract to the creamed butter mixture and beat for 1 minute until well combined. Pour in the dry ingredient mixture from Step 1 along with the milk and mix on low speed until just combined—don't overmix, as this can make the cookies tough. I like to finish mixing by hand with a spatula to ensure all the cocoa powder is fully incorporated without overdeveloping the gluten.

Roll the dough into 1-inch balls and coat each one by rolling in the remaining 1/3 cup granulated sugar. Place the sugar-coated balls on a parchment-lined baking sheet, spacing them about 2-3 inches apart. Refrigerate for at least 2 hours, or freeze for 1 hour if you're short on time. Chilling the dough prevents excessive spreading during baking and helps the cookies maintain their shape for the thumbprint indent.

Preheat your oven to 350°F while the dough chills. Once preheated, remove the chilled dough balls from the refrigerator and gently press your thumb or the back of a small spoon into the center of each cookie to create a thumbprint indent—don't press all the way through to the bottom. Bake for 12-14 minutes until the edges are set but the centers still look slightly underbaked. Remove from the oven and immediately press into the warm cookies again with your thumb to deepen the indent, then let cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.

While the cookies cool, prepare the ganache filling. Place the chopped semi-sweet chocolate in a heatproof bowl. Heat the heavy cream in a small saucepan over medium heat until it's steaming and just starting to simmer (don't let it boil). Pour the hot cream over the chocolate and let it sit undisturbed for 2-3 minutes—the residual heat will soften the chocolate. Gently stir until smooth and fully melted, then stir in the remaining 1/8 tsp peppermint extract. Let the ganache cool for about 10 minutes until it reaches a spoonable consistency but is still warm enough to settle nicely into the cookie indents.

Once the ganache has cooled slightly, spoon 1/2 to 1 teaspoon of the ganache into each cookie's indent. While the ganache is still soft, sprinkle the top of each filled cookie with crushed candy canes. I find that finely crushed candy canes mix in more evenly and look more elegant than larger pieces. Allow the ganache to set completely at room temperature or in the refrigerator for faster setting, and your peppermint bark thumbprint cookies are ready to enjoy!